Question: Simplify; express your answer in exponential form. Assume $r\neq 0, t\neq 0$. $\dfrac{{(r^{-2})^{4}}}{{(r^{-4}t^{-3})^{-3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${r^{-2}}$ to the exponent ${4}$ . Now ${-2 \times 4 = -8}$ , so ${(r^{-2})^{4} = r^{-8}}$ In the denominator, we can use the distributive property of exponents. ${(r^{-4}t^{-3})^{-3} = (r^{-4})^{-3}(t^{-3})^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(r^{-2})^{4}}}{{(r^{-4}t^{-3})^{-3}}} = \dfrac{{r^{-8}}}{{r^{12}t^{9}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{-8}}}{{r^{12}t^{9}}} = \dfrac{{r^{-8}}}{{r^{12}}} \cdot \dfrac{{1}}{{t^{9}}} = r^{{-8} - {12}} \cdot t^{- {9}} = r^{-20}t^{-9}$.